Stably stratified Taylor-Couette flow has attracted much attention due to its relevance as a canonical example of the interplay among rotation, stable stratification, shear and container boundaries, as well as its potential applications in geophysics and astrophysics. In this article, we review the current knowledge on this topic, highlight unanswered questions and propose directions for future research. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical transactions paper (Part 2)'.
Keywords: bifurcations; experiments; fluid dynamics; numerical methods.